Long-range predictability in the tropics
Part II: 30-60 day variability
Thomas Reichler
and John O. Roads
Scripps Institution of Oceanography
University of California San Diego, 9500 Gilman Dr., La Jolla, CA 92093-0224,
Correspondence to: John O. Roads (jroads@ucsd.edu)
Draft from Tuesday, January 21, 2003
The predictability of the tropical Madden-Julian oscillation (MJO) during 22 northern winter seasons (1979-2000) was investigated with six different ensemble experiments using the NCEP seasonal forecasting model. Each experiment was forced with a certain combination of initial and boundary conditions to examine the sensitivity of the simulated MJO to uncertainties in those conditions. The model simulated magnitude and spatial distribution of the intraseasonal variability quite well. About 10% of the model?s intraseasonal variability was caused by forcing with observed weekly sea surface temperatures (SSTs). When the model was forced with observed SSTs, it simulated a very reasonable MJO. The only shortcoming was that the spectral peak of the MJO was too broad. When climatological SSTs were used, the model produced an MJO at too high frequencies, indicating that the simulated MJO was sensitive to boundary forcing. When model, initial and boundary conditions were all perfect, the useful range of MJO predictability was about 4 weeks. This suggested that the MJO has the potential to improve long-range predictability. When using persisted instead of observed SSTs, the useful range reduced to about 3 weeks, and with climatological SSTs it was less than 2 weeks. The predictability of the MJO was insensitive to ENSO, but MJO predictability was higher when the MJO was more active. By decomposing the MJO into magnitude and phase of its wavenumber-one component, it was shown that the propagation of the MJO could be better predicted than its strength, but that imperfect boundary conditions affected mostly the propagation of the MJO, indicating that air-sea interaction was important for good simulation of the MJO propagation. Initial conditions affected the MJO out to 40 days. After this time, forcing with observed boundary conditions produced some small non-zero forecast skill. This boundary forced skill was particularly high during years with large intraseasonal SST energy. In a case study, the synchronizing effect of SST forcing on the phase of the MJO was demonstrated. By analyzing many MJO events it was shown that MJO and SST in nature were about 60? or 6-7 days out of phase, whereas in the model they were in phase. The consequences from this high sensitivity to boundary conditions are discussed.
2) External and internal variability
3.???? Simulated and observed intraseasonal
variability
b.??? Wavenumber-frequency spectra
4.???? Predictability of intraseasonal
variability
a.??? Lead time evolution of total intraseasonal predictability
c.??? Relationship between skill and activity
5.???? Phase space representation
b.??? Predictability of magnitude and phase
6.???? Forced intraseasonal variability
a.??? Tropical SST variability
1. Introduction
The intraseasonal or Madden-Julian oscillation (MJO) is the dominant mode of tropical low-frequency variability at periodicities between 30 and 60 days. It represents a substantial perturbation in the tropical wind field, which is manifested in other quantities like convective activity, cloud cover, and precipitation (Madden and Julian, 1994). It exhibits greatest variability over the Indian and western Pacific Oceans. The oscillation has predominantly a wavenumber-one structure, which propagates eastward along the equator at about 6 m/s in the Eastern Hemisphere and about 12 m/s in the Western Hemisphere (Waliser et al., 1999b). The slow evolution of the MJO relative to ?weather? and its importance for the tropical diabatic heating field suggest that the oscillation has the potential to improve long-range predictability (between two weeks and one season). For instance, Winkler et al. (2001) demonstrated with a linear model that the consideration of tropical heating, which is associated with the MJO and other effects, can produce predictability as far as seven weeks ahead. Another interesting aspect of the MJO is that it not only impacts the tropics, where the monsoon system or tropical cyclones are affected, but also the extratropics. Higgins and Mo (1997), for example, showed how the intraseasonal oscillation impacts extratropical weather through the creation of anomalies in the Hadley circulation and subsequent wave trains extending from the region of anomalous convection. Ferranti et al. (1990) found that the skill of medium range forecasts in the extratropics could be increased significantly with better representations of the MJO.
Although the intraseasonal oscillation may have the potential to improve long-range predictability, its practical realization is hampered by several factors. First, the MJO is not well understood, and several physical mechanisms have been proposed to explain it. Furthermore, cumulus convection, which is a key aspect of the MJO, is only crudely represented in current models. The consequence is that these models have substantial problems in simulating an adequate MJO (e.g., Slingo et al., 1996). The MJO is also difficult to predict because it is a very irregular occurring phenomenon. It has, for example, sporadic interannual variations, which are unrelated to boundary forcing (Slingo et al., 1999; Gualdi et al., 1999; Hendon et al., 1999; Waliser et al., 2001). This suggests that the nature of the oscillation is chaotic and essentially unpredictable. Additional complications arise from large errors which are contained in tropical analysis. They are related to the sparse observational network, and the lack of direct observations of divergence and diabatic heating, which are important for the simulation of the MJO (Hendon et al., 2000).
Relatively few studies examined the forecast skill of the MJO with dynamical models. Chen and Alpert (1990) investigated the predictability of the oscillation with the medium range forecast (MRF) model. Based on the filtered upper level velocity potential, they found that the spatial correlation coefficient of the MJO mode decays rapidly in time in the classical sense. If a correlation of less than 0.4 is considered useless, then the useful limit is reached at about 9 days. Similar results were reported by Lau and Chang (1992). Boer (1995) considered the wavenumber one component of unfiltered upper level velocity potential from ECMWF analysis and forecasts to study the predictability of the tropical divergent flow. The useful predictability range was also about 8 days during northern winter. More recently, Jones et al. (2000) examined the forecast skill of the MJO in a series of dynamical extended range forecast (DERF) experiments performed with the reanalysis version of the MRF model. They found that the forecast skill of filtered zonal winds at 200 hPa extended to about 8 day lead-time, and that it slightly increased for periods when the MJO was active.
The question, whether predictability increases when the oscillation is more active, is very controversial. For instance, Ferranti et al. (1990) found that the presence of strong MJO events significantly impacted extratropical predictability. Lau and Chang (1992) found also that the forecast error growth was smaller (larger) during periods of strong (weak) intraseasonal activity. However, Chen et al. (1993) found better predictability when the MJO activity was low. Boer (1995), on the other hand, reported little evidence that forecast skill depends on the state of the MJO. Hendon et al. (2000) found from DERF experiments that forecasts had even systematically lower skill during active episodes of the MJO as compared to quiescent times. They attributed this problem to the inability of the model to sustain the high level of MJO activity.
All the above studies agree surprisingly well that the dynamical predictability range of the MJO is about 8 days if a correlation of less than 0.4 is considered as useless skill. These relatively short predictability ranges do not really offer much hope to improve long-range predictability. They are also somewhat surprising, in particular when considering the time scale of the MJO and the intuitive notion that predictability for a given process should be approximately proportional to its life time (van den Dool and Saha, 1990). One of the problems of current models is simulating the correct propagation speed of the oscillation, which results in large phase decorrelation errors after relatively short time.
The previous predictability studies had two important things in common: First, forecasts were verified against observational data. Well known model deficiencies led to a dramatic decrease in predictability. Second, predictability was understood as a pure initial condition problem, but uncertainties in tropical analysis introduced errors into the forecasts. In addition, the role of air-sea interaction for the MJO was largely neglected. The DERF experiments from the National Centers for Environmental Predictions (NCEP), for example, used sea surface temperature (SSTs), which were damped to climatology from observed initial states with an e-folding time of 90 days (Schemm et al., 1996). It is, however, getting clearer that in addition to atmospheric internal dynamic instability, thermodynamic processes from the ocean interacting with the atmosphere may play an important role in sustaining the MJO. For instance, several previous studies found that coupling of the model atmosphere to simple ocean models, which allowed for feedbacks with the SSTs, improved the simulation of the MJO (e.g., Flatau et al., 1997; Waliser et al., 1999a). Flatau et al. (1997) speculated that increased MJO activity would result from warm SSTs to the east of the convective anomaly, which then would directly destabilize the atmosphere by increasing its moist static energy. Wang and Xie (1998) found that warm SST anomalies leading the convection anomalies acted to further reduce surface pressure, which increased convergence into the convective anomaly. Contrary to those studies, Hendon (2000) found little impact of coupling on the simulated MJO, but this may have been mainly due to unrealistic surface fluxes in his model. Very recently, Schubert and Wu (2001) and Wu et al. (2002) found from ensemble simulations from 10 different AGCMs during a specific 2 year period that prescribing observed weekly SSTs as boundary conditions on an atmospheric general circulation model (AGCM) led to significant MJO-like responses. The modeled SST influence seemed to be strongest over the Indian and western Pacific Ocean, where the MJO accounted in some models for more than 25% of the total intraseasonal variance.
To avoid the problems of previous studies, we asked what the predictability of the MJO would be if model, initial and boundary conditions would all be perfect. That is, we used a perfect model approach (Buizza, 1997; Anderson et al., 1999), where one forecast was verified against another forecast with the same model, and problems concerning uncertainties in the model formulation were thus completely eliminated. To further examine the influence of model errors on actual forecast skill, we also verified against reanalysis. We conducted six basic experiments with one particular AGCM using prescribed SSTs. The experiments differed only in the kind of initial and boundary conditions. Each experiment was carried out in a 10-20 member ensemble mode and simulated the northern winter atmosphere for 22 different years.
One of the goals of this study were to determine the inherent predictability properties of the MJO with perfect model and initial conditions. If the MJO is essentially chaotic and sensitively dependant upon initial condition perturbations, what is the time scale of deterministic predictability under perfect conditions, and how does it compare to real world forecasts? This research was also aimed at understanding how sensitive the simulated MJO was to uncertainties in initial and boundary conditions. In a companion paper (Reichler and Roads, 2003b), we investigated the predictability of monthly means in the tropics. The main difference between the two studies is variability on interannual time scales, which is contained in monthly means, but which has been eliminated in this study. For monthly means, boundary conditions are the main contributor to predictability. However, it was also found that even these longer-range forecasts were sensitive to initial conditions for many weeks. For forecasts of intraseasonal variability, good initial conditions are of course crucial, but how sensitive are MJO simulations to imperfect boundary conditions? This question is of practical importance since operational forecasts use SST boundary conditions which may contain large errors, either because simple methods like climatological or persisted SSTs are used, or because of the limitations of the ocean model. We were also concerned with the nature of the forced component of intraseasonal variability. We asked how much predictability was related to the forced response, and how model and real atmosphere were related to particular SST patterns.
The paper is structured as follows: Methodological aspects are discussed in section 2. The character and realism of the simulated intraseasonal variability is described in section 3. Section 4 describes the intraseasonal predictability for the different experiments. In section 5, the predictability of the MJO is described both for its propagation and as well as for its strength. In section 6, the forced component of intraseasonal variability and its relationship to SSTs is examined further. Summary and conclusions are presented in section 7.
2. Methodology
a. Model and experiments
The experiments of this study were carried out with the NCEP seasonal forecasting model (SFM). A detailed description of this model can be found in Kanamitsu et al. (2002b) as well as in Reichler and Roads (Reichler and Roads, 2003a). The model is based upon the 1995 version of the MRF model. The version for this study was released in October 2000. The SFM uses the spectral transform method to solve the primitive equations. A triangular truncation of 42 spherical harmonics (T42), equivalent to a horizontal resolution of about 280 km was chosen. For the simulation of the MJO, adequate vertical resolution may be crucial. For example Inness et al. (2001), who used the Unified Model with two different vertical resolutions (19 and 30 layers), demonstrated that the observed MJO variability could only be simulated by the AGCM with higher vertical resolution. The model of this study used a vertical sigma coordinate system which contains 29 layers. Another crucial element for the simulation of the MJO is the cumulus convection parameterization. The SFM employs the ?Relaxed Arakawa-Schubert? (RAS) scheme (Moorthi and Suarez, 1992), which is physically more realistic than the ?Simplified Arakawa-Schubert? (SAS) scheme (Grell, 1993) of the older reanalysis models.
The ensemble forecasts were carried out for 22 winter seasons from 1979 to 2000. Each forecast was initialized at December 15th and run continuously for 14 weeks until the end of the following March. The focus on the northern winter time was motivated by the heightened activity and most coherent eastward propagation of the intraseasonal oscillation during that time (e.g., Madden and Julian, 1994; Slingo et al., 1999). For each experiment and season, an ensemble of 10 forecasts were produced. For the reference experiment ICBC, the ensemble size was increased to 20. Simulations for each experiment, year and season were forced with identically evolving boundary conditions, but were started from slightly different initial conditions. The initial conditions were taken from special base runs (see below) or from reanalysis. Initial conditions were perturbed using the breeding technique (Toth and Kalnay, 1993; Toth and Kalnay, 1997), which calculates the fastest growing modes for a particular initial state from the atmospheric model. Details about the specific implementation of the breeding method are described in Reichler and Roads (Reichler and Roads, 2003a).
Table 1 summarizes the kind of experiments which were used in this study. Each experiment is designated by specific acronyms, which indicate the type of initial and boundary conditions and other variations. ?ICBC?, for example, means that perfect initial conditions (IC) and perfect boundary conditions (BC) were used. This will be described in more detail later. The experiments were performed globally, although the focus of this study was on the tropics. Two continuous base runs were performed first to derive initial conditions for the subsequent experiments. These base runs were similar in design to the Atmospheric Model Intercomparison Project (AMIP) (Gates, 1992). BASE‑O was forced with observed SSTs and sea ice, and BASE-C was forced with climatological SSTs and sea ice. Initial conditions from BASE-C are designated ?climatological?, and those from BASE-O ?anomalous?.
Experiment ICBC was forced with observed ocean boundary conditions, SSTs and sea ice. It was started from ?anomalous? initial conditions, which is equivalent to using ?observed? initial conditions under the perfect model assumption. Since both initial and boundary conditions were perfect, this gives the upper predictability limit of the MJO when verified against itself. Two more experiments were forced with perfect boundary conditions: Experiment BC, which was started from randomly chosen ?climatological? initial conditions. Experiment iBC was started from another long base run, which was initialized with slightly different initial conditions than BASE-O, but forced with the same observed ocean boundary conditions. Therefore, the initial conditions of iBC are similar to that of ICBC in the large scales, but not in the smaller scales. The motivation for this experiment was to find out how much predictability is lost by excluding the beneficial effects of synoptic scales in the initial conditions on dynamical predictability.
Another group of experiments started from perfect initial conditions, but were forced with less than perfect boundary conditions: Experiment IC was forced with climatological boundary condition. Experiment ICP was forced with persisted ocean boundary conditions, which means that the initial SST anomalies were simply persisted around the climatological seasonal cycle throughout the entire forecast. Persisted boundary conditions are a common alternative to more expensive dynamical ocean forecasts on time scales out to three months (e.g., Mason et al., 1999; Roads et al., 2001). Experiment CC started from ?climatological? initial conditions, and was forced with climatological boundary conditions. This provided us with a measure for the internally produced MJO variability without possible influences from boundary forcing.
b. Data
The NCEP/NCAR reanalysis (Kalnay et al., 1996; Kistler et al., 2001) were used to validate the model results. Global SST and sea ice data were prescribed as lower boundary conditions to the model experiments. Observational SSTs were taken from the UKMO Global Ice and Sea Surface Temperature (GISST) (e.g., Folland and Parker, 1995) data set for the 1948-1981 period, and from satellite-in situ blended SST analysis based on the method of optimum interpolation (Reynolds and Smith, 1994) after 1982. The sea ice distribution was taken from the NCEP/NCAR reanalysis. Some experiments were forced with a climatological seasonal cycle of SST and sea ice. Climatologies were calculated by averaging the observed monthly mean fields over the 50-year period 1950-1999, which were linearly interpolated to daily values. The climatology soil moisture and snow cover was derived from NCEP/DOE reanalysis-2 (Kanamitsu et al., 2002a) by averaging over the period 1979-1998.
Throughout
this study, the 200 hPa velocity potential was used as an indirect measure of
MJO activity. Velocity potential is commonly used in MJO studies, since
divergence and convergence of the wind field are associated with vertical
motions and convective activity. The velocity potential was derived by
decomposing the horizontal wind field v into rotational and divergent
parts, 
and 
, using the relationship
.???????????????????????????????????????????????????????? (1)
Here, _ is the velocity potential, and ` is the stream function. Since the gradient of _ gives the divergent flow, velocity potential represents the large scale aspects of the divergent flow. The 200 hPa level was used since it is approximately located at the maximum outflow of deep convective systems. Since the MJO was an equatorially trapped phenomenon, only data along the equator averaged from 10?N to 10?S were used. This latitudinal extent corresponds roughly to the equatorial Rossby radius, which is the natural length scale of dynamical systems at the equator (e.g., Gill, 1980). From now on, the 200 hPa velocity potential along the equator averaged from 10?N to 10?S will be simply designated _200.
c. Filtering
Before analyzing observational or simulated data, they were treated in the following way: The daily climatological mean annual cycle was first removed. The respective climatologies were calculated from each experiment by averaging over all years and ensemble members. We refer to these anomalies as unfiltered data. Next, the data were filtered in time by applying a 30-70 day band pass filter. The filtering was performed separately for each 107 day long forecast at each grid point over all ensemble members and years. Since the forecast time series were relatively short with respect to the time scales of the filter, the use of a filter with a sharp frequency response was problematic. Instead, the bandpass filtering was achieved by an iterative moving average procedure similar to that described by Waliser et al. (1999b). To remove variability longer than 70 days, a 25 day moving average filter was applied four times to each 107 day forecast. Each filtered time series became the input for the next pass. The smoothed time series was subtracted from the original data to remove variations of 70 days and longer. Then, a moving average filter of 9 days was applied four times to the new time series to remove variability of less than 30 days. The additional data at the beginning and end of the time series were generated by fitting at each pass of the moving average an autoregressive model of order 5 to the 107 days forecasts.
d. Analysis method
1) Measure of predictability
We measured predictability in terms of the spatial anomaly correlation (AC) over the equatorial domain between a prediction and a verification data set. As prediction data, 10-member ensemble means of the experiment under consideration were used. The ensemble mean provides in a statistical sense a more reliable forecast than any single forecast, since erroneous small scale structures are damped (e.g., Leith, 1974). Consequently, ensemble averaging increases predictability. To determine ?real world? skill, reanalysis was used as verification data. In most cases, however, the ?perfect world? skill was calculated by using experiment ICBC as verification. ICBC was used because its initial and boundary conditions were perfect. Since real world atmospheric states do not occur more than once, only single realizations of ICBC were taken. The average AC over each of the 20 individual members of ICBC was then the final result. Experiment ICBC was also verified against itself to measure the upper bound of predictability. In this case, again 10 instead of the possible 19 members were used to calculate the prediction ensemble mean. Another, arbitrarily chosen, member of ICBC was taken for the verification.
Since AC values are bounded by ?1, they can be non-normally distributed. Therefore, before adding or subtracting different ACs, we applied a Fisher Z transformation (e.g., Roads, 1988) to the ACs, that is,
.????????????????????????????????????????????????????????????????????? (2)
The final results were then again transformed back to normal correlations.
2) External and internal variability
The total variability of a climate quantity may be caused by external forcing from specified boundary conditions, or generated internally within the atmosphere. It is customary to call the two components signal and noise. From simulations with many ensemble members, Rowell (1995) suggested the signal should be calculated from the variability between ensemble means (intraensemble variance), and the noise from the variability between individual members around the ensemble mean (interensemble variance). The idea behind this concept is that the ensemble mean is ideally zero unless it is perturbed by external forcing, and that the spread of individual members around the ensemble mean is an estimate for the internal variability independent of boundary forcing. We followed this approach and estimated the internal variability by
,?????????????????????????????????????????????? (3)
where xyr is the quantity under consideration for year y and member r. Y is the number of years, and R is the number of members. The overbar denotes ensemble averaging. An estimate of the variability of the ensemble means is given by
,????????????????????????????????????????????????????????? (4)
where
the double bar denotes climatological ensemble mean. Because of the limited
number R of members which were used to compute the ensemble mean 
, the ensemble mean variance still contained some internal
variability and thus overestimated the SST forced variance. An unbiased
estimate of the external variability is given by
.?????????????????????????????????????????????????????????????????? (5)
Finally, we take
???????????????????????????????????????????????????????????????????????? (6)
to estimate the total variance of variable x. In the case of reanalysis only one member is available, so that the total variance is given by
.????????????????????????????????????????????????????????????? (7)
3. Simulated and observed intraseasonal variability
In the previous chapter, the general performance of the SFM model in the tropics was discussed in terms of its climatology and interannual variability. It was found that key-variables for tropical circulation compared well with observational data. Here, we assess the ability of the SFM model to simulate the MJO oscillation in order to provide a context for the subsequent results which were based primarily on model data. This is accomplished by presenting relevant characteristics of the simulated oscillation and by comparing it with observational data.
a. Analysis of variance
Fig. 1a presents the spatial distribution of total intraseasonal variability from simulations ICBC and IC in comparison to NCEP/NCAR reanalysis. Variances were calculated from intraseasonally filtered _200, as described in the previous section. Variances were calculated from daily data at lead times between 41 and 106 days, and the overall average is shown as final result. The first 40 days were excluded to avoid the deterministic predictability period which was influenced by initial conditions. The variance of the model was very similar to reanalysis in both magnitude and spatial distribution. Both indicate typical activity maximum over the Indian Ocean, and fewer activity over the Pacific Ocean. There was also increased activity over the Atlantic Ocean, which was more pronounced in the simulations than in the reanalysis. The main difference was that the simulated variance was somewhat larger than the observed one. Another difference was that the reanalysis exhibited one relatively broad center of activity over the Indian Ocean, whereas the simulations had two maxima. Simulation IC also had less variability than ICBC, indicating that boundary forcing increased total intraseasonal variability.
The ratio of external to internal intraseasonal variability for simulation ICBC and IC is shown in Fig. 1b. As expected from the climatological boundary forcing, simulation IC had no forced variability. Simulation ICBC, on the other hand, exhibited a signal to noise ratio of about 0.1. This value is relatively small compared to signal to noise ratios of 0.2-0.3 that were found by Wu et al., 2002 from 10 different AGCMs over two full years. This demonstrated clearly that boundary forcing did affect intraseasonal variability, but also that this effect was rather small. The forced variability was higher over the Indian Ocean region, which coincides with the region of increased convective activity.
b. Wavenumber-frequency spectra
Fig. 2 shows wavenumber-frequency spectra of _200 for NCEP/NCAR reanalysis, as well as for experiments ICBC and IC. The spectra were calculated from daily fields, individually for each members and year. The final results shown in Fig. 2 are averages over all years and members. In the reanalysis (Fig. 2a), the eastward propagating wavenumber one was the largest component. It had a broad spectral peak centered at 54 day period, which is traditionally attributed to the MJO phenomenon. The secondary maximum at zero frequency corresponds to the seasonal mean, since interannual variability was not removed from the data. The spectrum from the perfect experiment ICBC (Fig. 2b) showed less concentration of energy on a single wavenumber as the reanalysis. Nevertheless, most energy was in the eastward going wavenumber-one component, and there was a secondary peak at about the same period as reanalysis. The spectrum for simulation IC (Fig. 2c) contained less energy than ICBC at the very low frequencies. This was mainly a consequence of using climatological instead of observed SSTs, which eliminated most of the interannual variability. The spectral peak of IC at 36 days was at a higher frequency than observed, which is a typical problem for many AGCMs (e.g., Hayashi and Golder, 1993; Kuma, 1994; Slingo et al., 1996). It is interesting, however, that the forcing with observed SSTs reduced somewhat this problem, as the spectrum from simulation ICBC demonstrates. This indicates that the MJO of this model was sensitive to boundary forcing.
c. Composite MJO
Further characteristics of the MJO in reanalysis and model can be gathered from the time-longitude representation of composite events (Fig. 3). The composites were calculated by averaging over the n strongest MJO events based on the value of filtered _200 at 150?E. Taking into account the different ensemble size of the data sets, n was 20 for reanalysis, 200 for ICBC, and 100 for IC. The strength of the MJO for reanalysis and simulations was very similar, but the activity in the simulations tended to be spatially more localized than in the reanalysis. The composites allowed an estimate of the average periodicity of the MJO. It was about 41 days for reanalysis, 40 days for ICBC, and 31 days for IC, which again indicated that the use of observed SST forcing leads to more realistic simulations of the MJO.
Overall, these results demonstrated that the SFM was able to simulate a reasonable MJO when it was forced with observed SSTs. The model shows a clear eastward propagating signal with reasonable strength and periodicity. The main shortcoming was that the model was not able to simulate the dominance of the intraseasonal oscillation at periods of 50 days. It simulates too much power at higher frequencies, in particular when it was forced with climatological SSTs, again which is typical of many AGCMs.
4. Predictability of intraseasonal variability
a. Lead time evolution of total intraseasonal predictability
In this section, we describe the perfect model predictability of the MJO and its sensitivity to initial and boundary conditions. This was accomplished by examining the spatial anomaly correlation (AC) for the various experiments as a function of lead time. Daily fields of intraseasonally filtered _200 were used for the AC calculation. Fig. 4 shows the evolution of the ACs from initialization (Dec. 15th) out to day 106 (March 31st) for the five experiments.
Fig. 4a shows ACs averaged over all 22 years (1979-2000) years. Simulation ICBC, verified against itself (continuous line), provides the upper predictability limit of the MJO. Model, initial and boundary conditions were all perfect, except for small perturbations in the initial conditions. These perturbations grew through non-linear chaotic interactions and led to divergence of the various forecasts. The curve for ICBC shows the classical loss in predictability with forecast range. If a correlation of 0.4 is taken as the minimum for useful skill, then the limit of MJO predictability is reached at about 4 weeks. This range was much longer than the 8 day limit found from previous studies. The main reason for this difference are not due only to the perfect conditions for experiment ICBC, but also because some other methodological differences like meridional and ensemble averaging. After 30-40 days or so, deterministic predictability of ICBC was completely lost, and the skill reached a constant value of about 0.2. This small but nevertheless non-zero skill is due to the effects of boundary forcing on intraseasonal variability. Simulations iBC and BC, which started from imperfect initial conditions, but which were forced with the same perfect boundary conditions, showed similar correlations at this long lead. This result confirms the non-zero signal to noise ratio, which was found in the previous section from simulation ICBC.
The range of useful predictability for ICP (dashed-dotted curve), as measured by a correlation of 0.4, extended to about three weeks. This was roughly one week less as compared to having perfect boundary conditions, but it was still much longer than 8 days reported from previous studies. ICP reached zero skill at about 40 days, indicating that the effects of forced and initial condition predictability were both zero at this time. The skill of experiment IC, which was forced with climatological initial conditions, decayed even faster. This was presumably due to the adjustment of the atmosphere to climatological boundary conditions and its impact on the MJO. The useful limit was reached after only 9 days, and zero skill was reached at about 30 days. The differences in predictability between ICBC and ICP, and between ICBC and IC showed very clear that the simulation of the MJO was sensitive to boundary forcing. Overall, these results indicate that air-sea interaction is potentially important for the simulation of the MJO.
We were also interested in finding out whether strong boundary forcing from the El Ni?o Southern Oscillation (ENSO) phenomenon affected the predictability of the MJO. In the past, the demonstration of a connection between ENSO and MJO has been somewhat controversial. Some studies suggested that the activity of the MJO was controlled by ENSO (e.g., Gutzler, 1991; Fink and Speth, 1997), while others found little evidence for such a link (e.g., Slingo et al., 1999; Hendon et al., 1999). We repeated the calculation of the ACs by averaging only over weak-to-neutral ENSO years. Strong cold and warm ENSO years during the 1979-2000 period were those listed in Table 2; neutral-to-weak ENSO years were all the other years. The classification of ENSO years was taken from the Climate Prediction Center at NCEP (published on the internet), which provides a season-by-season breakdown of the SST conditions of the tropical Pacific. Fig. 4b shows the average evolution of predictability during those years. Since fewer years were included in the average, the curves were somewhat noisier than before. However, the ACs of the various experiments were very similar to using all years, and showed no evidence that the state of ENSO might have had any effects on the predictability of the MJO.
To find out more about the role of initial and boundary conditions in producing MJO predictability, we calculated the ACs for experiment IC and CC verified against themselves and compared the skill with ICBC verified against itself (Fig. 5). Since each experiment was verified against itself, boundary and initial conditions were perfect in each case. Remember, the only difference between IC and CC are the initial conditions: IC was initialized from anomalous, and CC from climatological initial conditions. During the initial 30 days, the skill of IC was almost identical to ICBC. This suggests that strength and structure of anomalous boundary forcing has little influence on the predictability of the MJO at this time range. Experiment CC, on the other hand, shows clearly lower predictability as compared to ICBC. This suggests that initial conditions do impact the predictability of the MJO. As we will see later, this is probably related to the level of MJO activity at the beginning of the forecast, since activity is correlated to predictability.
We also examined the predictability of simulations ICBC-r and IC-r verified against reanalysis. The comparison between ICBC-r and ICBC gives an estimate of how strong the model related error component is. Fig. 6a shows forecast skill computed from _200. The unsmoothed results for ICBC-r and IC-r (thin curves) are very noisy, since only one realization (the real atmosphere) was used as verification. Therefore, it is better to study the smoothed (thick) curves instead. To the extent that the smoothed results were representative, the skill of ICBC-r was very similar to that of ICBC. This is somewhat surprising, and means that model related errors are not very large. This may be related to the fact that the divergent circulation is not an observed quantity. Therefore, velocity potential may be strongly influenced by the assimilation model of the reanalysis, which may have similar biases as the AGCM of this study. We therefore repeated the calculations of predictability by replacing _200 with zonal winds at 200 hPa (u200). Since winds are observed, they should be closer to real observations in the reanalysis. Fig. 6b shows the results for u200 from ICBC-r and ICBC, each verified against itself. For ICBC, the predictability of u200 was very similar to that of _200, at all lead times. The difference between ICBC-r and ICBC shows that model related errors are now more important. The limit of useful skill for ICBC-r was reached at about 20 days, whereas that for ICBC extended out to 27 days. Also the purely forced part of predictability at long lead times was lower for ICBC-r than for ICBC.
b. Interannual variations
Fig. 7 presents a year by year
breakdown of intraseasonal predictability. This breakdown allowed us to
identify years where predictability was particularly high or low, and to find
out how important initial and boundary conditions were during those years. As
before, we analyzed the intraseasonal anomalies over some lead time interval
during individual years, measured from filtered _200.
As discussed before, the effects of initial
conditions on intraseasonal predictability lasted on average for about 40 days.
Consequently, predictability was analyzed separately for a short lead time
interval (day 0-40), where deterministic predictability from perfect initial
conditions was high, and a long lead time interval (day 41-106), where the
initial condition effect was small and the forced variability of the MJO was
important.
Fig. 7a presents the average ACs during the short lead time interval for the three experiments ICBC, IC, and ICP, which were started from perfect initial conditions. The perfect experiment ICBC (black bars) exhibits a rather large interannual variability in predictability, implying a possible dependence on the particular flow state. During some years (e.g., ?88, ?96), the forecast skill from initial conditions alone (simulation IC, green bars) was surprisingly close to that of ICBC. This indicates that the MJO was a very robust feature during those years. During other years (e.g., ?83, ?89, ?93), however, simulation IC shows much smaller skill than ICBC, indicating that the MJO can be very sensitive to additional uncertainties introduced by boundary forcing. The correlations for experiment ICP (blue bars) usually followed very closely those of ICBC, which suggests that the results were very robust and reproducible. On the other hand, correlations from ICP were also consistently smaller than ICBC, indicating how important boundary forcing for the MJO was.
The year to year variations in predictability for the long lead time interval (day 49-106) are shown in Fig. 7b. Only the results for experiments ICBC, iBC and BC are presented, since they were forced with perfect boundary conditions. At this long lead time interval, predictability resulted only from the forced intraseasonal response. As expected, the skill of ICBC was generally lower than at the short lead time interval. However, there were some years (e.g., ?90, ?92) during which the ACs were remarkably high. Results for BC and iBC followed closely those of ICBC, which was consistent with the common effects of boundary forcing.
c. Relationship between skill and activity
As mentioned before, the relationship between forecast skill and the activity of the intraseasonal oscillation is somewhat controversial. Some studies found that forecast skill increased when the MJO was more active, whereas others found the opposite, or no relationship. We examined this relationship for experiment ICBC. Fig. 8 shows for individual years the spatio-temporal variance of bandpass filtered _200. Variance was calculated in space along the equator and in time from forecast day 0-40 (a) and 41-106 (b). There exists a modestly good relationship between year to year variations of predictability and activity, as can be seen by comparing with Fig. 7. The correlation for the short lead time interval was 0.6, and for the long lead time interval 0.48. Both correlations were statistically significant at the 95% error level.
5. Phase space representation
In the following, the MJO is investigated in Fourier space in terms of the complex expansion coefficients of the wavenumber one component. From the spectral energy distribution presented before it is clear that most of the intraseasonal energy of _200 was contained in this wavenumber. In fact, wavenumber one was often taken as the defining parameter for studies of the MJO (e.g., Lorenc, 1984; Slingo and Madden, 1991; Boer, 1995). The advantage from the spectral representation is that the spatial _200 field is represented by just two real variables, the phase and magnitude of its wavenumber one component. The phase represents the propagation of the intraseasonal oscillation, and the magnitude its strength or activity. The idea behind this approach is somewhat similar to the decomposition into two eigenmodes, which was more widely used in previous MJO studies (e.g., Lorenc, 1984; Chen and Alpert, 1990; Ferranti et al., 1990; Jones et al., 2000). The Fourier decomposition of intraseasonally filtered _200 in the east-west direction along the equator is defined by
,??????????????????????????????????????????????????????????? (8)
where zm are complex Fourier expansion coefficients and m the wavenumber. The complex wavenumber one coefficient can be also written in polar coordinates,
z1 = r exp(i^). ???????????????????????????????????????????????????????????????????????????? (9)
Then, the magnitude r represents the strength of the oscillation, and the phase ^ the propagation. From the magnitudes, anomalies with respect to the 1979-2000 climatology were calculated. When correlations are calculated, the 2X-periodicity of the phases would lead to problems. This was avoided by representing the phase angles by
?> = sin(^) . ??????????????????????????????????????????????????????????????????????????? (10)
Note that this definition could lead to some ambiguity because of the cyclic nature of the sine function.
a. Case studies
Phases and magnitudes of the MJO during 1992 are examined here in more detail. From the annual breakdown of predictability it is known that during 1992 the forecast skill of experiment ICBC was moderately high for the short (0.6 correlation), and unusually high for the long (0.55 correlation) lead time interval. Fig. 9 presents for the five experiments the evolution of filtered _200 in terms of wavenumber-one magnitude and phase. Each panel shows the evolution of _200 from individual members (thin lines) as well as ensemble means (thick lines). The ensemble means show variability which is common to all members, either because of the initial condition memory, or because of the effects of boundary forcing. From the spread of individual members around the mean one can estimate how certain an individual forecast was.
The phases > for the five experiments are shown in the left panels of Fig. 9. At short leads, phases of individual members of ICBC, IC and ICP tended to be similar because of the initial condition effect. The phases of experiments iBC and BC, which started from different initial conditions than ICBC, were less coherent, and did not agree well with ICBC. Out to very long lead times, individual members of IC showed a relatively high degree of coherence, even so they were forced with climatological SSTs. This can also be seen from the regular oscillations of the ensemble mean. During the 107 day long simulation there was an approximate passage of 3.5 MJO cycles, corresponding to a mean period of about 30 days. Experiments with observed SSTs had a longer periodicity. This has already been noted in the previous discussion of the spectra. The spread for experiment ICP was very large, in particular after day 30. Experiment ICBC indicated additional interesting behavior. At forecast day 30 or so, the phases transitioned into a different cycle. After that, individual members were again in very good agreement. At the same time, the phases of iBC and BC also agreed well with ICBC, in particular during forecast days 40-80. As we will show later, this synchronizing effect was related to strong intraseasonal SST activity during that time. The right panels of Fig. 9 present the evolution of the magnitude anomalies r. Magnitudes had less coherence than the phases. The ensemble means varied close around zero, which corresponds to the climatological mean. Only experiments ICBC, iBC and BC exhibited some increased activity during the second half of the forecast.
Let us now focus on the ensemble mean response. In this case, a phase space representation is advantageous, because it allows the combination of magnitude and phase in a single graph. Consider first the situation for 1992 (Fig. 10a). Shown is the evolution of the wavenumber-one Fourier coefficient of filtered _200 in the complex plane, where the magnitude r is represented by the distance to the origin, and the phase ^ by the angle from the positive x-axis. Time is indicated by different colors. The similarity between trajectories of individual experiments is a measure of predictability. At short lead times (0-20 days, red and orange colors), the trajectories of ICBC, IC, and ICP were quite similar. After that, experiment IC had continuous regular oscillations but the magnitude decreased because of the gradual decorrelation of individual members. The trajectory of ICP was very distorted at longer lead times (green and blue colors), since the coherence between members was lost. Experiment ICBC exhibited the already mentioned regime shift at about day 30 (yellow color), and then continued with regular oscillations. After the shift, the trajectories of iBC and BC were very similar in phase as well as in magnitude to ICBC, owing to the strong forced variability in all three experiments.
As another example, Fig. 10b presents the MJO evolution during 1996. From Fig. 7 one can see that during this year initial condition (0.5 correlation) as well as boundary forced predictability (0.4 correlation) was modestly high. Similar as before, the trajectories of ICBC, IC and ICP agreed well at short leads (red colors). At longer leads, IC continuous to oscillated quite regularly and performed about 3.5 oscillations. As before, simulation ICBC exhibited a regime shift at about day 20 (yellow color), and at longer leads (greenish and bluish colors), the trajectories of ICBC, iBC and BC were quite similar.
b. Predictability of magnitude and phase
Fig. 11 presents predictability of magnitudes r (a.) and phases > (b.) as a function of lead time. Predictability at a certain lead time was measured from the temporal correlation between a prediction and a verification time series, which consisted of the year to year variations in r or > at this lead. As before, 10 members ensemble means of the corresponding experiment were used as prediction data, and individual members of simulation ICBC were used as verification data. The overall lead time evolution of predictability for r and > was similar to that of total predictability (Fig. 4). Boundary forcing, for example, led to non-zero forecast skill at long lead times for both r and >, as can be seen from the results for experiments ICBC, iBC, and BC. r and > had characteristic differences in terms of their predictability. Phases were generally better predictable than magnitudes. In other words, the propagation of the intraseasonal oscillation was better predictable than its strength. This may be related to the slow propagation of the intraseasonal oscillation, which causes a high degree of persistence in its phase. Simulation ICP reveals another interesting phenomenon: Uncertainties associated with the use of persisted ocean boundary conditions impacted mostly the phase of the MJO. This indicates that the propagation speed of the intraseasonal oscillation was particularly sensitive to boundary forcing.
6. Forced intraseasonal variability
In this section, the relationship between SST forcing and intraseasonal variability is examined in more depth. It was shown before that boundary forcing affected intraseasonal activity, and that it led to long lead predictability with an average correlation of 0.2. However, there were considerable year to year variations, and during certain years, the forced variability could be strong and important for predictability. The previous analysis showed that for example 1990, 1992, 1996 and 2000 were such years. Therefore, most of the following analysis was focused on those years.
a. Tropical SST variability
SST patterns with a similar spatio-temporal structure as the MJO are very effective in forcing atmospheric intraseasonal variability, much in the sense of resonant forcing of a dynamical system. From observational studies it is known that tropical SSTs have an intraseasonal peak (e.g., Krishnamurti et al., 1988). This peak is coherent with observed changes in surface heat fluxes and SSTs that occur during the passage of an MJO (e.g., Zhang, 1996; Flatau et al., 1997; Maloney and Kiehl, 2002). Local SST variations in association with the passage of an MJO can reach 1.0?C and more (Weller and Anderson, 1996). We investigated space-time spectra of the SSTs seen by experiment ICBC to find out whether there were any links to predictability. Before the spectra were computed, the annual mean as well as the annual and semi-annual seasonal cycle were removed from the SST data. In space, spectra were calculated along the equator. This was repeated for all latitudes between 10?N and 10?S, and the final results were averaged over those latitudes. Fig. 12 presents for each year the amount of SST energy in the 54 day band. Shown are averages for the eastward traveling wavenumbers 0-3. Clearly, 1992 contained the maximum energy of all years. The comparison with Fig. 8b shows that long-lead intraseasonal predictability was usually higher during years with larger intraseasonal SST energy. The correlation between both quantities was 0.58. This was relatively high, in particular when considering that such a relationship was not necessarily linear, and that other factors beside SST forcing determined predictability as well.
b. Case study
Next, the situation for 1992 was studied in more detail. Fig. 13 presents a one by one comparison of tropical SST anomalies and associated intraseasonal activity from reanalysis (a) and simulation ICBC (b). The SSTs, which are shown by shading, are identical in both panels and represent latitudinal averages from 10?N to 10?S. The SSTs exhibited the typical signature of an ENSO warm event, with warmer waters over the Pacific, and colder waters over the warm pool region. Superimposed on this mean pattern is strong intraseasonal SST variability. The overlaid black contour lines show the evolution of the MJO as given by filtered _200. The reanalysis (Fig. 13a) exhibited a good relationship between SST anomalies and MJO activity. SSTs were warmer before the period of active convection (negative _200) and cooler after it. Simulation ICBC (Fig. 13b) showed also a clear MJO signal, which seemed to be shifted by about 1 quarter cycle towards earlier times with respect to the reanalysis. This led to a more direct relationship between SST and MJO activity, in the sense that anomalous rising motions tended to coincide directly with warm or neutral SST anomalies, and sinking motions with cold SST anomalies. This good relationship suggest that SST forcing with proper frequencies can phase lock the simulated MJO into its own cycle.
The intraseasonal SST variations over the warm pool region amount only to 0.6?C or so. It is interesting that such small variations in temperature could control the intraseasonal activity in the model. To explain this behavior it is important to understand that the atmospheric response to tropical SSTs is strongly non-linear. Observations show that SSTs above 26-27?C are required for large-scale deep convection to occur, and that little convective activity takes place over SSTs colder than that (e.g., Graham and Barnett, 1987). Since the mean SSTs over the Indian Ocean during January were close to the 27?C threshold, even small anomalies were effective in controlling convective activity.
c. SST-MJO relationship
A more general relationship between SST and MJO is derived from composites of many MJO events. The contours in Fig. 14 show composites of strong MJO events for simulation ICBC (top panels) and for reanalysis (bottom panels). Similar as in Fig. 3, the composites were formed by selecting the n strongest MJO events from intraseasonally filtered data over a specific base point. Two different base points, one over the Indian Ocean (90?E) and one over the warm pool (150?E), were selected to capture different stages of the MJO. The SSTs are shown by shading. As shown in all four panels, the SSTs exhibited strong intraseasonal variability, even though data were unfiltered. This indicates again that intraseasonal SST variability was associated with similar variability in the atmosphere. The SSTs for the reanalysis had more noise than the simulation because of the smaller sample size. In the model (top panels), convection was again enhanced (suppressed) by warm (cold) SST anomalies almost directly underneath. In the reanalysis (bottom panels), the regions of warmest SST anomalies tended to lead the convective anomalies by several days.
To better quantify the relationship between MJO and SST, cross-correlations between the composite MJO and associated SST anomalies were calculated for different phase lags (Fig. 15). Temporal correlations were computed between the filtered _200 time series at a fixed grid point and SST anomaly time series at different positions to the east or west of the point. Results from all grid points along the equator were averaged. For the reanalysis (continuous lines), the MJO had the strongest negative correlations with SSTs at a phase lag of about 60?E or about 7 days. The two different base points lead to very similar results. The correlations are negative since cool (negative) SST anomalies tend to suppress convection, which leads to positive velocity potential anomalies (upper level convergence). The 60? phase shift agrees well with the general picture seen before: SSTs are higher before the period of active convection and lower after it. This is also in line with observational findings from Flatau et al. (1997), which showed that to the east of the area of active convection, in the convergence region of a Kelvin wave, increased downward fluxes of shortwave radiation in conjunction with mostly cloud free conditions generated positive SST anomalies. In the vicinity of enhanced convection, cloud shielding and strong air-sea sensible and latent heat fluxes cooled the local SSTs. To the west of the convection, enhanced latent heat fluxes associated with increased surface westerlies tended to further cool the SSTs. For simulation ICBC (dashed lines), maximum negative correlations occurred for SST anomalies at phase lags of only about 10?E. This much smaller eastward shift reflects the different MJO-SST relationship between model and nature. In nature, SST variations are caused by the MJO as outlined above. In the model, however, prescribed SSTs force the atmosphere above, so that the simulated MJO tends to be almost in phase with the SST. These results are also in line with Wu et al. (2002), who found that simulated and observed velocity potential anomalies tend to be in quadrature with the simulations leading the observed anomalies by about 10 days.
7. Summary and conclusion
This study investigated the predictability of the tropical intraseasonal oscillation and its sensitivity to initial conditions and boundary forcing. Six types of AGCM experiments were conducted with the NCEP SFM, each with different combinations of initial and boundary conditions. Each experiment simulated the state of the northern winter atmosphere over the 22 year long period from 1979-2000 in a 10-20 member ensemble mode. The results were mainly based on the intraseasonally filtered 200 hPa velocity potential in the tropical sector.
The interannual variability in the model was very similar to reanalysis. When forced with observed weekly SSTs, the model exhibited a intraseasonal signal-to-noise ratio of about 0.1. This showed that most of the model?s intraseasonal variability was created by internal atmospheric dynamics, and that only a small portion was related to thermodynamic forcing from the ocean. The MJO of the model was quite realistic when forced with observed weekly SSTs. The model MJO showed a clear eastward propagating signal with reasonable strength and periodicity. The main shortcoming of the model was that the spectral peak of the oscillation was broader than in the reanalysis. When forced with climatological SSTs, the spectral peak of the simulated MJO shifted toward higher frequencies. This problem is typical for many AGCMs, and indicates that the MJO of the model is sensitive to boundary forcing.
Perfect model predictability was derived from the spatial anomaly correlation between two forecasts. With perfect initial and boundary conditions, the useful range of MJO predictability, as given by a correlation of 0.4, averaged out to 4 weeks. Considering that the MJO has global implications, this relatively long time scale indicates that good forecasts of the MJO would have the potential to improve long-range predictability. Simulations of the MJO were very sensitive to the quality of boundary conditions. When using persisted instead of observed SSTs, the range of useful predictability was reduced to about 23 days, and with climatological SSTs it was less than 10 days. Including only years of neutral-to-weak ENSO events into the calculation of the ACs showed no evidence that ENSO forcing might affect the predictability of the MJO. There were also strong interannual variations in predictability. During some years, initial conditions alone led to very robust MJO simulations, while in other years, boundary conditions were more important for good predictability. It was found that the activity of the MJO was one factor which influences predictability, in the sense that predictability was higher when the MJO was more active.
Phase and amplitude of the wavenumber-one component were used to characterize dynamics of the MJO. This had the advantage that the main features of the MJO, its propagation and strength, were expressed by two separated variables. Under the influence of boundary forcing intraseasonal variability could be so strong that MJOs of individual members stayed in phase at very long lead times. Using this decomposition, the predictability of phase and strength of the MJO was further investigated. The phase was more predictable than the strength. It was argued that this is related to the relatively slow propagation speed of the MJO. It was also shown that uncertainties in boundary conditions affected mostly the phase or propagation of the MJO, and to a lesser extent its activity. This was consistent with results from the spectral analysis, and underlined the role of air-sea interaction as a controlling element for the propagation of the MJO.
The effects of initial conditions on the simulation of the MJO lasted for a maximum of about 40 days. After this period, forcing with observed boundary conditions still produced some skill, as was to be expected from the non-zero signal-to-noise ratio. This boundary forced predictability amounted on average to 0.2 correlation, but there existed large interannual variations. The spectral analysis of observed tropical SSTs revealed a positive relationship between frequency of the SST forcing and intraseasonal predictability. During years where the SST energy in the intraseasonal band was high, the forced intraseasonal response of the atmosphere was high, and so was predictability. In a case study, the relationship between SST forcing and MJO was examined in more detail. During the northern winter of 1992, intraseasonal activity in the real atmosphere produced strong intraseasonal variability in the tropical SST field. In the model, these prescribed SST variations phase locked the MJO into a cycle similar to the observations. The general relationship between MJO and SST was investigated from composites of many MJO events. In nature, intraseasonal SST anomalies are usually caused by MJO activity, and SSTs are higher before the period of active convection and lower after it. The phase lag between both is about 60? longitudes or about 7 days. In the model, however, SST anomalies forced intraseasonal variability. Therefore, MJO and SST tended to be more in phase, with enhanced convection almost directly above positive SST anomalies.
The study found evidence that the simulated intraseasonal variability responds to prescribed SST forcing. This results is consistent with other studies (e.g., Wu et al., 2002), and suggests that coupling with the ocean may be important for the simulation of the MJO. The forced predictability, which was found from prescribing weekly SST observations, does of course not imply the same predictability under real conditions. The problem is that SSTs themselves are to some extent product of the unknown atmospheric forcing. Real predictability may only be possible to the extent that the atmosphere is sensitive to persistent preexisting SST anomalies, for example from previous MJO events. Nevertheless, this study gave clear evidence that the MJO has the potential to improve long-term predictability if good initial and boundary conditions can be obtained. Persisted or climatological boundary conditions are not sufficient to produce good long-term simulations of the MJO. The coupled nature of the MJO requires boundary conditions which can evolve and interact with the atmosphere in time. Further progress in the long-range predictability effort may therefore be achieved with fully coupled models.
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Table 1: Boundary and initial conditions, ensemble size and simulation period for each experiment and the two base runs. ?r-2? means NCEP/DOE reanalysis-2. Winter refers to Dec. 15th ? Mar. 31st of the following year. ?rndm.? indicates randomly chosen initial conditions, ?obs.? means observational data (reanalysis-1), ?cont.? indicates continuous simulations over all years, and ?clim.? indicates climatological boundary conditions.
Table 2: Classification of strong ENSO years during January
1979-2000.
Fig. 1: Total variance (left) and ratio of external to internal variance (right) of filtered _200 from individual members. Shown are averages over all years and members, and over days 40-106 of each season. Units of variance are 1012 m4s-2.
Fig. 2: Wavenumber-frequency spectra of unfiltered _200 from daily fields of individual members for the 1979-2000 period: (a) from NCEP-NCAR reanalysis, (b) from experiment ICBC, and (c) from experiment IC. Units are 1012 m4s-2 day. Contour levels are 50, 100, 200, 300, 400, 500 and 600. Shading indicates values greater than 200.
Fig. 3: Composite MJO events in Hovm?ller representation, derived from filtered _200. Composites were calculated by averaging over n strongest events based on the value of _200 at 150?E. n was taken 20 for reanalysis, 200 for ICBC, and 100 for IC. Units are 106 m2s-1. Contour levels are from ?9 to 9 in steps of 2. Negative values are dashed, and positive values are contoured continuously.
Fig. 4: Predictability as function of lead time as measured by the spatial anomaly correlation of filtered _200: (a) are averages over all years, and (b) are averages over neutral-to-weak ENSO years only. Vertical axis denotes correlation (AC).
Fig. 5: As in Fig. 4 but for experiment IC and CC verified against themselves. The skill from ICBC is shown as reference.
Fig. 6: (a) As Fig. 4 but for experiment ICBC-r and IC-r verified against reanalysis. The skill from ICBC is shown as reference. (b) Predictability of filtered zonal wind at 200 hPa for experiment ICBC-r verified against reanalysis, and ICBC verified against itself.
Fig. 7: Predictability during individual years as measured by the spatial anomaly correlation (calculated as Fig. 4), averaged over forecast day 0-40 (a) and 41-106 (b). Ordinate denotes AC, and abscissa denotes year of the January of the forecast.
Fig. 8: Annual MJO activity as measured by the spatio-temporal variance of filtered _200 from experiment ICBC. Variance was calculated in space along the equator and in time from forecast day 0-40 (a) and 41-106 (b). Ordinate denotes variance in 1012 m4s-2. In the top left corner, correlation between activity and predictability from Fig. 7 is shown.
Fig. 9: MJO evolution during northern winter 1992 as measured by the magnitude and sine of the phase of wavenumber-one filtered _200. Thin lines denote individual ensemble members (20 for ICBC, else 10), and thick lines show ensemble mean. Magnitudes indicate anomalies from climatology with units 106 m2s??-???1.
Fig. 10: Trajectory of the MJO in phase space. Shown is the evolution of the complex wavenumber-one coefficient of filtered _200 during northern winter 1992 (a) and 1996 (b) for different experiments. Distance from the center denotes magnitude in 106 m2s?????1 (see ICP). Angle from the positive x-axis represents phase. Time is shown in colors and by numbers for ICBC (1992). It changes every 5 days, starting with red (day 0-4), and ending with purple (day 105-107). The geographical locations mark the approximate center of maximum convection for a given phase angle.
Fig. 11: Predictability of magnitude (a) and phase (b) of
wavenumber one filtered _200 as
function of lead time, and as measured by the temporal correlations. The curves are smoothed
with a 21 days moving average filter. Vertical axis denotes correlation.
Fig. 12: Variability of tropical SSTs during northern winter at 54 days period, summed over eastward traveling wavenumbers 0-3. Units are K2 day.
Fig. 13: Unfiltered SST anomalies during 1992 in time-longitude representation. Units are in ?K. Black contours show filtered _200 from reanalysis (a) and ICBC (b).
Fig. 14: Composite MJO events (contours) and associated SST anomalies (shading) for simulation ICBC (top panels) and reanalysis (bottom panels). Shown are composites of 200 (ICBC) or 10 (reanalysis) strongest MJO events, as given by negative anomalies of filtered _200 at the base point (90?E left panel, 150?E right panel). Contour interval is from ?6-6?106 m2s-1 in intervals of 2. Negative values are dashed. SST anomalies are standardized by the local interannual standard deviation.
Fig. 15: Temporal correlation between composite MJO and SST (as shown in Fig. 14) for base points at 90?E (a) and 150?E (b). Ordinate denotes temporal correlation, and abscissa denotes west- or eastward shift of SSTs.
Table 1: Boundary and initial conditions, ensemble size and simulation period for each experiment and the two base runs. ?r-2? means NCEP/DOE reanalysis-2. Winter refers to Dec. 15th ? Mar. 31st of the following year. ?rndm.? indicates randomly chosen initial conditions, ?obs.? means observational data (reanalysis-1), ?cont.? indicates continuous simulations over all years, and ?clim.? indicates climatological boundary conditions.
|
|
boundary conditions |
initial conditions |
|
|
|
||
|
name |
ocean |
land |
atmosphere |
land |
size |
period |
years |
|
BASE-O |
observed |
model |
obs. 1/1/48 |
obs. 1/1/48 |
1 |
cont. |
1948-2000 |
|
BASE-C |
clim. |
model |
obs. 1/1/48 |
obs. 1/1/48 |
1 |
cont. |
1948-2024 |
|
ICBC |
observed |
model |
BASE-O |
BASE-O |
20? ? |
winter |
1979-2000 |
|
ICP |
persisted |
model |
BASE-O |
BASE-O |
10? ? |
winter |
1979-2000 |
|
IC |
clim. |
r-2 clim. |
BASE-O |
- |
10 |
winter |
1979-2000 |
|
ICBC-r |
observed |
r-2 |
r-2 |
- |
10? ? |
winter |
1979-2000 |
|
IC-r |
clim. |
r-2 clim. |
r-2 |
- |
10 |
winter |
1979-2000 |
|
BC |
observed |
model |
BASE-C rndm. |
BASE-C rndm. |
10 |
winter |
1979-2000 |
|
iBC |
observed |
model |
ICBC, 1 yr lag |
ICBC, 1 yr lag |
10 |
winter |
1980-2001 |
Table
2: Classification of strong ENSO years during
January 1979-2000.
|
ENSO event |
January |
|
cold |
1985, 1989, 1999, 2000 |
|
warm |
1983, 1987, 1992, 1998 |
Fig. 1: Total variance (left) and ratio of external to internal variance (right) of filtered _200 from individual members. Shown are averages over all years and members, and over days 40-106 of each season. Units of variance are 1012 m4s-2.
Fig. 2: Wavenumber-frequency spectra of unfiltered _200 from daily fields of individual members for the 1979-2000 period: (a) from NCEP-NCAR reanalysis, (b) from experiment ICBC, and (c) from experiment IC. Units are 1012 m4s-2 day. Contour levels are 50, 100, 200, 300, 400, 500 and 600. Shading indicates values greater than 200.
Fig. 3: Composite MJO events in Hovm?ller representation, derived from filtered _200. Composites were calculated by averaging over n strongest events based on the value of _200 at 150?E. n was taken 20 for reanalysis, 200 for ICBC, and 100 for IC. Units are 106 m2s-1. Contour levels are from ?9 to 9 in steps of 2. Negative values are dashed, and positive values are contoured continuously.
Fig. 4: Predictability as function of lead time as measured by the spatial anomaly correlation of filtered _200: (a) are averages over all years, and (b) are averages over neutral-to-weak ENSO years only. Vertical axis denotes correlation (AC).
Fig. 5: As in Fig. 4 but for experiment IC and CC verified against themselves. The skill from ICBC is shown as reference.
Fig. 6: (a) As Fig. 4 but for experiment ICBC-r and IC-r verified against reanalysis. The skill from ICBC is shown as reference. (b) Predictability of filtered zonal wind at 200 hPa for experiment ICBC-r verified against reanalysis, and ICBC verified against itself.
Fig. 7: Predictability during individual years as measured by the spatial anomaly correlation (calculated as Fig. 4), averaged over forecast day 0-40 (a) and 41-106 (b). Ordinate denotes AC, and abscissa denotes year of the January of the forecast.
Fig. 8: Annual MJO activity as measured by the spatio-temporal variance of filtered _200 from experiment ICBC. Variance was calculated in space along the equator and in time from forecast day 0-40 (a) and 41-106 (b). Ordinate denotes variance in 1012 m4s-2. In the top left corner, correlation between activity and predictability from Fig. 7 is shown.
Fig. 9: MJO evolution during northern winter 1992 as measured by the magnitude and sine of the phase of wavenumber-one filtered _200. Thin lines denote individual ensemble members (20 for ICBC, else 10), and thick lines show ensemble mean. Magnitudes indicate anomalies from climatology with units 106 m2s??-???1.
Fig. 10: Trajectory of the MJO in phase space. Shown is the evolution of the complex wavenumber-one coefficient of filtered _200 during northern winter 1992 (a) and 1996 (b) for different experiments. Distance from the center denotes magnitude in 106 m2s?????1 (see ICP). Angle from the positive x-axis represents phase. Time is shown in colors and by numbers for ICBC (1992). It changes every 5 days, starting with red (day 0-4), and ending with purple (day 105-107). The geographical locations mark the approximate center of maximum convection for a given phase angle.
Fig. 11: Predictability of magnitude (a) and phase
(b) of wavenumber one filtered _200 as
function of lead time, and as measured by the temporal correlations. The curves are smoothed
with a 21 days moving average filter. Vertical axis denotes correlation.
Fig. 12: Variability of tropical SSTs during northern winter at 54 days period, summed over eastward traveling wavenumbers 0-3. Units are K2 day.
Fig. 13: Unfiltered SST anomalies during 1992 in time-longitude representation. Units are in ?K. Black contours show filtered _200 from reanalysis (a) and ICBC (b).
Fig. 14: Composite MJO events (contours) and associated SST anomalies (shading) for simulation ICBC (top panels) and reanalysis (bottom panels). Shown are composites of 200 (ICBC) or 10 (reanalysis) strongest MJO events, as given by negative anomalies of filtered _200 at the base point (90?E left panel, 150?E right panel). Contour interval is from ?6-6?106 m2s-1 in intervals of 2. Negative values are dashed. SST anomalies are standardized by the local interannual standard deviation.
Fig. 15: Temporal correlation between composite MJO and SST (as shown in Fig. 14) for base points at 90?E (a) and 150?E (b). Ordinate denotes temporal correlation, and abscissa denotes west- or eastward shift of SSTs.